can I add a mailing list to my site?

I would like to have a small mailing list embedded in my website/blog. I need, say, 20 to 30 people to be in it. is this at any rate possible with a widget, or any other tool provided in the wordpress.com environment?

Since WordPress.com does not have email servers, that's not possible here. Use the contact form to get people to sign up for a mailing list that you create somewhere else where you have an email account.

It sounds to me like you are asking if you can distribute an email newsletter by emailing your material to a particular email address and then have it distributed to a mailing list. If you set up "post by email" on your site, your posts will be distributed to your readers depending on how they have chosen to receive your new posts (email, Reader, RSS, etc.) http://en.support.wordpress.com/post-by-email/

Before you set up Post by Email, just make sure that you have a secure email client with a strong password which you are not using anywhere else on the web. Post by Email seems to be vulnerable when people are ignorant about password security.